1/2x-4=2x+3-5/2x

Solution for 1/2x-4=2x+3-5/2x equation:

1/2x-4=2x+3-5/2x

We move all terms to the left:

1/2x-4-(2x+3-5/2x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(2x-5/2x+3)-4=0

We get rid of parentheses

1/2x-2x+5/2x-3-4=0

We multiply all the terms by the denominator


-2x*2x-3*2x-4*2x+1+5=0

We add all the numbers together, and all the variables

-2x*2x-3*2x-4*2x+6=0

Wy multiply elements

-4x^2-6x-8x+6=0

We add all the numbers together, and all the variables

-4x^2-14x+6=0

a = -4; b = -14; c = +6;
Δ = b2-4ac
Δ = -142-4·(-4)·6
Δ = 292
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{73}}{2*-4}=\frac{14-2\sqrt{73}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{73}}{2*-4}=\frac{14+2\sqrt{73}}{-8}
$